论文标题
随着任意周期性的Stokes流量的快速Ewald总和
Fast Ewald summation for Stokes flow with arbitrary periodicity
论文作者
论文摘要
提出了一种快速且精确的Ewald求和方法，用于评估三维Stokes流的Stokeslet，压力和Rotlet电位。这项工作扩展了先前开发的光谱ewald方法，用于在统一框架中以任何数字（三，两个，一，一个或无）流向周期性边界条件。周期电势被分成一个短距离和一个远距离部分，其中后者使用快速傅立叶变换在傅立叶空间中处理。该方法的关键组成部分是用于治疗单数集成的修饰核。我们得出了新的修改核，并为Stokeslet和压力点进行了新的改进的截断误差估计。设计和测试了基于给定的错误公差选择参数的自动化过程。提出了用于验证的分析公式，以双重和单一的周期性案件进行验证。我们表明，对于N来源和目标，方法量表（如O（n log n））的计算时间，并研究时间如何取决于误差耐受性和窗口函数，即用于平滑不规则点数据的函数到均匀的网格。该方法在完全周期性的情况下最快，而自由空间中的运行时间约为大约三倍。此外，将方法应用于较低纵横比的原代细胞中均匀的源分布时达到的效率最高。本文介绍的工作能够使用例如使用例如，例如使用例如边界积分和潜在方法。
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for Stokes flow to periodic boundary conditions in any number (three, two, one, or none) of the spatial directions, in a unified framework. The periodic potential is split into a short-range and a long-range part, where the latter is treated in Fourier space using the fast Fourier transform. A crucial component of the method is the modified kernels used to treat singular integration. We derive new modified kernels, and new improved truncation error estimates for the stokeslet and stresslet. An automated procedure for selecting parameters based on a given error tolerance is designed and tested. Analytical formulas for validation in the doubly and singly periodic cases are presented. We show that the computational time of the method scales like O(N log N) for N sources and targets, and investigate how the time depends on the error tolerance and window function, i.e. the function used to smoothly spread irregular point data to a uniform grid. The method is fastest in the fully periodic case, while the run time in the free-space case is around three times as large. Furthermore, the highest efficiency is reached when applying the method to a uniform source distribution in a primary cell with low aspect ratio. The work presented in this paper enables efficient and accurate simulations of three-dimensional Stokes flow with arbitrary periodicity using e.g. boundary integral and potential methods.
